Some parents live vicariously through their kids. That means they live their lives through the activities of their children. For example, a father wanted to be a major league baseball player when he was young. He never quite had the skills to make it, so he pushes his son to practice hard so that his son can make it to the big show one day...whether his son aspires to that or not. Or a mother always wanted to be a ballet dancer when she was young, so she pays an exorbitant amount for lessons so her daughter can perform with a prestigious dance company some day and tour the world.
One definition of the word “vicarious” is “to experience secondhand.” That fits the descriptions of the aforementioned parents. Another definition is “suffered or done by one person as a substitute for another.”
That second description fits the entire life of our Lord Jesus. His entire life was “lived vicariously.” All that he did he did for us, as our substitute (Gal. 4:4-5). He willingly, perfectly obeyed God the Father's will. Not once did Jesus ever slip and break any of the 10 Commandments in thought, word, or deed. And all this he did in your place and mine.
Likewise, Jesus willingly laid down his life at the cross as the perfect, holy, righteous sacrifice for the sins of the world (1 Pet. 1:18-19). You and I deserve to die and be eternally separated from God because of our sins. You and I deserved to be on Calvary's cross. But Jesus died there in our place, as our substitute (Is. 53:4-5; 2 Cor. 5:21). He endured death and the pain of being separated from his Father at the cross, and he cried out, “My God! My God! Why have you forsaken me?” (Matt. 27:46)
On the third day, Jesus rose to life again...vicariously. His resurrection was for us, too. Because he lives, we too shall live (John 14:19; Rom. 6:4-5). His resurrection is the start of the new creation that you and I enjoy right now...a life of reconciliation and relationship with God (2 Cor. 5:17). But we are not yet bodily raised to life, as Jesus is. For us, our resurrection will happen on the Last Day when Jesus returns (1 Thess. 4:16).
It's probably not a healthy thing for parents to live vicariously through their kids. Living that way may lead to unhealthy expectations, psychological damage, and family conflict.
But it's a good thing that we have someone who lived vicariously for us...Jesus, our Savior. Joined to his vicarious life through baptism, all that he accomplished in his death and resurrection becomes ours. God now sees you as perfect and holy. You are seated with Christ in the heavenly realms (Eph. 2:6). The riches of heaven are yours. And in this way, you might say that you are “living vicariously” through Jesus, because he is your substitute.
So live “vicariously.” Live knowing you are God's baptized child. Live knowing you are forgiven. Live knowing that you are reconciled to God. Live knowing that you are a new creation now. Live feeding on the body and blood of your Risen Savior. And live looking forward to the resurrection to eternal life on the Last Day.